Define Entropy Change

Define Entropy Change :

In this section we define the entropy changes s that occurs when a closed system changes from a well-defined final state by a process, that we can describe as reversible.

One mole of ideal gas is confined to the left-hand side (as drawn) of a thermally isolated container, and occupies a volume Vo. The right hand side of the container, also containing a volume Vo, is evacuated. The tap (solid line) between the two halves of the container is then suddenly opened and the gas fills the entire container, of volume 2Vo.

We propose that both the previous and new temperature and pressure follow the Ideal Gas Law, so that initially we have PiVi=RTi and then, when the tap is opened, we have PfVf=RTf, where R is the ideal gas constant.

As the system is thermally isolated, it cannot exchange heat with its surroundings. Also, since the system's volume is kept constant, the system does not do work on its surroundings. As a result, the change in internal energy 0, and because the internal energy is a function of temperature only for the ideal gas, we know that Thus the pressure halves; i.e.

For an ideal monatomic gas, the entropy as a function of the internal energy.

This result is also valid if the gas is not monatomic, as the volume dependence of an ideal gas in the dilute limit (in which classical statistical mechanics correctly describes the translational degrees of freedom) is the same as for a monatomic gas.

One can also evaluate the entropy change using purely thermodynamic methods. It is necessary to then take another route from the initial state to the final state, such that all the intermediary states are in thermal equilibrium.

This means that such a route can only be realized in the limit where the changes happen infinitely slowly. Such routes are also referred to as quasistatic routes.

In some books one demands that a quasistatic route has to be reversible, here we don't add this extra condition.

The net entropy change from the initial state to the final state is independent of the particular choice of the quasistatic route, as the entropy is a function of state.

The Second law of Thermodynamics

Entropy And The Second law of Thermodynamics : 

We can imagine many processes that never happen; even they do not violate the law of conservation of energy. For instant, hot coffee resting in a mug might give up some internal thermal energy and spontaneously began to rotate.

Entropy is a thermodynamic property that can be used to determine the energy not available for work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when converting energy to work. During this work, entropy accumulates in the system, which then dissipates in the form of waste heat. 

Thermodynamics is the branch of physical science concerned with heat and its relation to other forms of energy and work. It defines macroscopic variables, that describe average properties of material bodies and radiation, and explains how they are related and by what laws they change with time.

Thermodynamics does not describe the microscopic constituents of matter, and its laws can be derived from statistical mechanics.

 For thermodynamics and statistical thermodynamics to apply to a process in a body, it is necessary that the atomic mechanisms of the process fall into just two classes: those so rapid that, in the time frame of the process of interest, the atomic states effectively visit all of their accessible range, and those so slow that their effects can be neglected in the time frame of the process of interest.The rapid atomic mechanisms mediate the macroscopic changes that are of interest for thermodynamics and statistical thermodynamics, because they quickly bring the system near enough to thermodynamic equilibrium.

 "When intermediate rates are present, thermodynamics and statistical mechanics cannot be applied."

 The intermediate rate atomic processes do not bring the system near enough to thermodynamic equilibrium in the time frame of the macroscopic process of interest. This separation of time scales of atomic processes is a theme that recurs throughout the subject.